Numerical Methods at work

Disclaimer:
Permission to use, copy, and distribute this software, and It’s documentation for any non-commercial purpose is hereby granted without fee, provided: THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL Henrik Vestermark, BE LIABLE FOR ANY SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER ADVISED OF THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

Numerical Integration

This web calculator performed numerical integration using well-known numerical integration methods:
  • Trapez
  • Romberg
  • Simpson
  • Fox-Romberg
  • Gauss-Legendre
  • Gauss-Chebyshev
  • Gauss-Hermite
  • Double Exponential
Image of Numerical integration
Numerical Integration & Graphing. vs. 1.12

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Integration Method






 


  • Results
  • Graphing
  • Convergence
  • Delta-E
  • Help

Help

Explanation: Enter the equation that needs to be displayed. The usual math function can be used: +.-.*,/,(,), abs(), acos(), asin(), atan(), atan2(), cos(), exp(), log(), pow(), sin(), sqrt(), tan(). Note for x^3 used the pow(x,3) notation and log() is the natural logarithm
If you need integration as well, checkmark on one or more integration methods. For the fastest and most accurate method use Fox-Romberg, Double exponential, or Gauss.
For accuracy, the method takes it to the numeric limits, however, to avoid time-consuming operations the limits on number function evaluation is around 65536 calls.
Note: Gauss-Chebyshev required that the function is on form f(x)/sqrt(1-x^2) otherwise result are incorrect. Gauss-Hermite required that the function is on the form e-x^2*f(x).
The Test button set up a default equation (for testing only). Note that the interval [0,0.5] contains a singularity for x=0 making it hard for Trapez, Simpson, and Romberg method to get high accuracy on the result. Fox-Romberg can handle this to the numeric limit!
Email: hve@hvks.com if you have any questions.
This version has been tested with Edge, Chrome, Firefox & Safari browsers.
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Corrections:
6-Feb-2025vs 1.12Disable autocapitalization, autocorrection and spellcheck for the input fields. Furthermore math.js library allows expressions in the input fields.
17-Nov-2023vs 1.11Switch to the Plotly library and remove the display option which is redundant with the Plotly package
8-Nov-2019vs 1.10Redesign the GUI
17-Oct-2019vs 1.9Fixed some display errors in the HTML code.
25-Nov-2011vs 1.8Layout changes and switching to using canvas objects for HTML graphics. Now Print also print the Graphic of the Function, Convergence Power, and Delta-E values
28-May-2011vs 1.7Fixed an issue with prematurely stop of the integration resulting in the wrong result. This was demonstrated with f(x)=x-floor(x) in [0,6.4]
04-May-2011vs 1.6Added Email and rearranged the layout
15-Nov-2009vs 1.5Added Double Exponential integration method
21-May-2007vs 1.4Added Gauss-Hermite integration
17-May-2007vs 1.3Added Gauss-Chebyshev integration and more display options
09-May-2007vs 1.2Added Gauss-Legendre integration method
23-Apr-2007vs 1.1Initial release